Eur. Phys. J. D (2012) 66: 309
https://doi.org/10.1140/epjd/e2012-30308-9

Regular Article

On the electrodynamics in time-dependent linear media

Departamento de Física, Universidade Federal da Paraíba Caixa Postal 5008, 58051-970 João Pessoa, Paraíba, Brazil

^a e-mail: arosas@fisica.ufpb.br

Received: 14 May 2012
Received in final form: 13 September 2012
Published online: 4 December 2012

Abstract

In this work we study the classical electrodynamics in homogeneous conducting and nonconducting time-dependent linear media in the absence of charge sources. Surprisingly, we find that a time dependence in the permittivity gives rise to an additional term in the Ampere-Maxwell equation and the presence of extra terms, non-analogous between themselves and proportional to first or even second derivatives of dielectric and magnetic permittivities in the electric and magnetic field wave equations. We consider a linear and an exponential growth of the permittivity, as well as a sinusoidal time-dependent permittivity, as special cases, obtaining the time-dependence of the electromagnetic fields.